유수 정리 (residue theorem)
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개요
- 복소함수론의 주요 정리 중 하나
응용
\[\sum_{k=1}^{\infty}\frac{1}{k^{4}-a^4}=\frac{1}{2a^4}-\frac{\pi \cot (\pi a)}{4 a^3}-\frac{\pi \coth (\pi a)}{4 a^3}\] \[\sum_{n=-\infty}^{\infty}\frac{1}{n^2+n+1}=\frac{2\pi \tanh \left(\frac{\sqrt{3} \pi }{2}\right)}{\sqrt{3}}\]
역사
메모
관련된 항목들
수학용어번역
- residue - 대한수학회 수학용어집
사전 형태의 자료
노트
말뭉치
- Applying the Cauchy residue theorem.[1]
- The integral over this curve can then be computed using the residue theorem.[2]
- The new winding number allows to establish a generalized residue theorem which covers also the situation where singularities lie on the cycle.[3]
- This residue theorem can be used to calculate the value of improper integrals for which the standard technique with the classical residue theorem does not apply.[3]
- In the present article, we introduce a generalized, non-integer winding number for piecewise cycles and a general version of the residue theorem which covers all cases of singularities on .[3]
- Definition 2 of a generalized winding number turns out to be useful as it allows to generalize the residue theorem (see Theorem 8 below).[3]
- The Espil's theorem it's a short proof of the Cauchy's generalized residue theorem.[4]
- However, I decided to use the nuclear bomb of the integration arsenal, the Cauchy residue theorem of complex analysis.[5]
- In an upcoming topic we will formulate the Cauchy residue theorem.[6]
- 1 Residue theorem problems 2 2 Zero Sum theorem for residues problems 76 3 Power series problems 157 Acknowledgement.[6]
- The following result, Cauchy’s residue theorem, follows from our previous work on integrals.[6]
- Using residue theorem to compute an integral.[6]
소스
메타데이터
위키데이터
- ID : Q830513
Spacy 패턴 목록
- [{'LOWER': 'residue'}, {'LEMMA': 'theorem'}]
- [{'LOWER': 'cauchy'}, {'LOWER': 'residue'}, {'LEMMA': 'theorem'}]
- [{'LOWER': 'cauchy'}, {'LOWER': "'s"}, {'LOWER': 'residue'}, {'LEMMA': 'theorem'}]